CN108536971A - A kind of Structural Damage Identification based on Bayesian model - Google Patents
A kind of Structural Damage Identification based on Bayesian model Download PDFInfo
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Abstract
The invention discloses a kind of Structural Damage Identification based on Bayesian model, step includes：First, single Measuring Point Structure that observation obtains is decomposed using Empirical mode decomposition to respond to obtain time-varying intrinsic mode function to construct the likelihood function of Bayesian model, gradation type Markov chain Mondicaro algorithm is used during the likelihood function of the Bayesian model of the time-varying intrinsic mode function responded based on single measuring point system structure is designed for Bayesian model update method, avoid from be difficult sampling model Posterior probability distribution in direct sample, but it is sampled from a series of simpler intermediate probability distribution for converging on Posterior probability distribution, and it can automatically select intermediate probability density function using this method and directly acquire the normalized parameter in model parameter Posterior probability distribution formula, computational efficiency greatly improved.
Description
Technical field
The invention belongs to monitoring structural health conditions fields, relate generally to a kind of Damage Assessment Method side based on Bayesian model
Method.
Background technology
As urban land resource is more in short supply in recent decades, skyscraper and high-rise building are built on a large scale
As the important directions of the contemporary development of building trade both at home and abroad.Skyscraper and high-rise building its during use, due to length
Phase is acted on by load and environment, and the continuous aging of its structural material, component damage are constantly accumulated as time increases, structure
Bearing capacity be constantly lower so as to cause building structure performance reduce even destroy, seriously threaten the people's lives and property
Safety.Therefore, Damage Assessment Method is carried out to skyscraper and high-rise building, and structure is likely to occur dangerous and bad
Situation, which carries out security evaluation and the condition of a disaster early warning, critically important realistic meaning.
The current existing damnification recognition method based on statistical analysis technique mainly has traditional probability statistical method, probability god
Through network method, statistical system identification method etc..Traditional probability statistical method is based on existing sample observations, and structure is suitable
Estimator and hypothesis testing method with calculate unknown parameter statistical value, but while choosing test statistics due to it, is often very tired
Difficulty, the information that the priori of parameter can not be utilized also not consider that subsequent samples provide, the application of this method have limitation.Probability
Neural network method is developed from the bayesian criterion of multivariable pattern classification, and Bayesian Estimation is coupling in Feedforward Neural Networks
In network, estimate that carrying out Bayesian decision obtains classification results, can handle observation data according to the printenv of probability density function
Containing in the case of noise pollution damage mode identification or classification problem.But probabilistic neural network method there are still convergence,
The problems such as network model selects and network size determines.Statistical system identification method can be summarized as STOCHASTIC FINITE ELEMENT Modifying model
Two class method of method and Bayesian model revised law.For STOCHASTIC FINITE ELEMENT Modifying model method, if there is sufficient amount of structure is rung
Data, model error and observation noise should be observed to be influenced to drop by observing the statistical average of data to corrected parameter
It is low, but due to that can only obtain limited observation data under physical condition, the method is by taking the photograph observation data and model parameter
Dynamic stochastic simulation obtains the probabilistic statistical characteristics of system model parameter.The analysis result that this method perturbs for one order
Often local convergence, and its result is influenced very big by the selection of initial parameter values, while larger range of parameter perturbation can be bright
The aobvious precision for reducing this method, therefore STOCHASTIC FINITE ELEMENT Modifying model method is larger in the upper limitation of application.Bayesian model is repaiied
The uncertainty of the probability distribution quantitative description structural model using model parameter is executed, then according to the given letter of observation data
Breath corrects the relatively uncertain of different initial models, then by solution so that the optimization problem determination of cost function minimum is repaiied
Optimum structure model after just finally compares optimum structure model model parameter probability distribution corresponding with benchmark architecture to realize
Damage Assessment Method.Compared with classical statistics estimating method, the maximum difference of this method be to take full advantage of structural model and
The prior information of predicated response is constantly updated the probability distribution of model parameter by the observation data of structural response, model is joined
Several priori probability density functions is converted into the posterior probability density function of model parameter.But traditional bayes method is past
Toward normalized parameter that can not be in solving model parameter Posterior probability distribution formula, need to be asked using Markov chain Mondicaro method
The approximate solution for solving Posterior probability distribution is solved with the complexity of structural model and increase this method of unknown parameter quantity
Calculation amount and degree of difficulty can greatly increase, and the expression formula that can not obtain likelihood function can limit the practicality of this method significantly
Property.Therefore, it is necessary to propose that new Bayes's damnification recognition method improves traditional bayes method, to propose rational likelihood
Function expression, while the efficiency for calculating response sample is improved, to solve the problems, such as practical civil engineering.
Invention content
In order to solve the problems in the existing technology, the present invention proposes a kind of structural damage based on Bayesian model
Recognition methods, the time-varying intrinsic mode function tectonic model likelihood function that this method is responded using single Measuring Point Structure, while in shellfish
Gradation type Markov chain Mondicaro algorithm is used during this model modification of leaf, can be greatly reduced in Practical Project and identify
The computational complexity of damage is built, the efficiency of building non-destructive tests is improved, is economized on resources and the time for engineering construction.
The present invention uses following technical scheme：
A kind of Structural Damage Identification based on Bayesian model, this approach includes the following steps：
S1, the system structure for being detected to obtain multigroup single measuring point to mechanical structure or building structure respond；According to going through
The prior probability distribution of history data setting system structure parameter, it is intrinsic according to gaussian probability profile set list measuring point acceleration responsive
The prior probability distribution of the prediction error variance of mode function；
S2, the system structure that single measuring point is decomposed using Empirical mode decomposition respond to obtain its intrinsic mode function,
Utilize the probability density estimation of the intrinsic mode function structure forecast error vector；
S3, Definition Model group parameter set a series of model groups to be selected, and close using the probability of the prediction error vector
Spend the likelihood function that function model derives construction Bayesian model；
S4, the intrinsic mode function obtained based on the decomposition, are applied to gradation type by the likelihood function derived
Markov chain Mondicaro (TMCMC) algorithm designs Bayesian model update method, based on the system structure for detecting and obtaining
Response updates the prediction error of the system structure parameter and single measuring point acceleration responsive intrinsic mode function of the model group to be selected
The prior probability distribution of variance, the posteriority for calculating the corresponding normalized parameter of each model group to be selected and model parameter are general
Rate is distributed, and finally acquires in a series of model groups to be selected the most model group of possibility by Bayesian model method for selecting,
Obtain the Posterior probability distribution of the corresponding system structure parameter of the most probable model group；
S5, referred to according to the damage of the Posterior probability distribution structural texture of the corresponding system structure parameter of the most probable model group
Mark, judges structural damage.
Further, the specific implementation method of the step S1 includes：
Setting models group Mk(subscript k indicates the serial number of model group), it is assumed that D={ y(l):L=1 ..., NeIt is comprising NeGroup
The observation data of system response, model parameter vector θ ∈ Θ ∈ RNpIt is intrinsic by system structure parameter and single measuring point acceleration responsive
The prediction error variance of mode function is constituted, and the prior probability distribution of the system structure parameter, root are set according to historical data
According to the prior probability point of the prediction error variance of single measuring point acceleration responsive intrinsic mode function described in gaussian probability profile set
Cloth, thus set the model parameter vector prior probability distribution p (θ | Mk)。
Further, the specific implementation method of the step S2 includes：
Assuming that the model output of structure is expressed as model (θ), corresponding system output is expressed as system, then predicting
Error vector can be calculated by e=system-model (θ), according to principle of maximum entropy, predict the probability density function of error vector
Model is the Gaussian Profile for having zero-mean and covariance matrix, is constructed using the intrinsic mode function of single Measuring Point Structure response pre-
Survey the probability density estimation of error vector：
Wherein i=1 ..., the serial number of n expression intrinsic mode functions, subscript l=1 ..., NeIndicate the sequence of observation experiment
Number, subscript r indicates single Measuring Point Structure response, can be acceleration (a), speed (v) or dynamic respond (d),It is first
The prediction error vector of i-th of intrinsic mode function of single Measuring Point Structure response in observation experiment, No is the degree of freedom observed
Quantity,For the prediction error variance of i-th of intrinsic mode function of single Measuring Point Structure response, teIndicate the time point measured
Quantity, t indicate the time point serial number measured,It is the of the structural response that t moment in first of observation experiment observes
I intrinsic mode function, IMFi mr(θ, t) is the model value of i-th of intrinsic mode function of the structural response of t moment,For list
The prediction error variance of i-th of intrinsic mode function of Measuring Point Structure response.
Further, the specific implementation method of the step S3 includes：
Definition Model group parameter：
Wherein standard deviationStd () indicates the standard deviation of signal.For a series of
Model group M, the factor η and ρ can define a series of model group M={ M to be selectedk=M (η (k), ρ (k)):K=1 ..., Nc,
Assuming that the prediction error of system response is statistically independent of one another, then likelihood function can be expressed as
Wherein overall fit measure definitions are
C is mark Huaihe River constant, can be derived and be calculated according to formula (1)-(3).
Further, the specific implementation method of the step S4 includes：
On the basis of likelihood function model, according to Bayes principle, the Posterior probability distribution of model parameter vector can be by
Following formula is derived：
Wherein p (θ | Mk) be model parameter vector priori probability density function, p (D | Mk) it is normalized parameter；
Formula (3)-(5) are applied to gradation type Markov chain Mondicaro (TMCMC) algorithm, to a series of model group M
Based on the system structure response progress Bayesian model update for detecting and obtaining, the corresponding normalizing of each model group can be obtained
Change the Posterior probability distribution of parameter and model parameter；
It is assumed that all model groups have equally probable prior probability, then the probability density function of prior distribution is by p (Mk
| M)=1/NcIt calculates, and normalized parameterOn this basis, by Bayes's mould
Type method for selecting：
Most probable model group can be acquired, the Posterior probability distribution { θ of the corresponding system structure parameter of the model group is obtaineds,h:h
=1 ..., Ns, subscript h indicates to follow the serial number of the structural parameters sample of Posterior probability distribution.
Further, the specific implementation method of the step S5 includes：
In view of the different damage modes of structure, structure is obtained under different damage modes by the step S1 to S4
The Posterior probability distribution of the corresponding system structure parameter of most probable model groupComparison structure is not
The posterior probability density function for the corresponding system structure parameter of most probable model group estimated under degree of impairmentStructural texture damage criterion IOD (Index of damage) judges the position of structural damage
And degree of injury：
Wherein, subscript j=1 ..., NdIndicate different damage modes.
Compared with prior art, advantageous effects of the invention are as follows：
The present invention provides a kind of Structural Damage Identifications based on Bayesian model, can be applied to multi-Degree-of-Freedom Linear
The structural parameter identification of time-varying system and small nonlinearity time-varying system.The parameter identification method of traditional time-invariant system is often adopted
Likelihood function is constituted with the intrinsic frequency and Mode Shape of system, the present invention proposes novel likelihood function model, uses list
The time-varying intrinsic mode function tectonic model likelihood function of Measuring Point Structure response, time-varying intrinsic mode function can be easily from corresponding
The empirical mode decomposition of structural response obtains, and can be used for solving the parameter identification problem of general time-varying system, significantly reduces meter
Calculate complexity.
Meanwhile the present invention uses gradation type Markov chain Mondicaro algorithm in Bayesian model renewal process, keeps away
The problem directly sampled from Posterior probability distribution is exempted from, from a series of simple intermediate probability for converging on Posterior probability distribution
It is sampled in distribution, can directly acquire the normalized parameter in model parameter Posterior probability distribution formula, improve the effect of calculating
Rate.
By the Structural Damage Identification for implementing to provide in the present invention, it can be greatly reduced in Practical Project and identify structure
The difficulty of damage improves the efficiency of Damage Assessment Method, economizes on resources and the time for engineering construction, makes subsequent engineering construction more
Carry out smoothly and more quickly.
Description of the drawings
Fig. 1 is a kind of step schematic diagram of heretofore described Structural Damage Identification based on Bayesian model.
Specific implementation mode
In order to be fully understood from the purpose of the present invention, feature and effect, below with reference to attached drawing and specific implementation mode pair
The technique effect of design, specific steps and the generation of the present invention is described further.
As shown in Figure 1, the invention discloses a kind of Structural Damage Identification based on Bayesian model, step packet
It includes：
S1, the system structure for being detected to obtain multigroup single measuring point to mechanical structure or building structure respond；According to going through
The prior probability distribution of history data setting system structure parameter, it is intrinsic according to gaussian probability profile set list measuring point acceleration responsive
The prior probability distribution of the prediction error variance of mode function；
Specifically, the specific implementation method of step S1 includes：
Setting models group Mk(subscript k indicates the serial number of model group), it is assumed that D={ y(l):L=1 ..., NeIt is comprising NeGroup
The observation data of system response, model parameter vector θ ∈ Θ ∈ RNpIt is intrinsic by system structure parameter and single measuring point acceleration responsive
The prediction error variance of mode function is constituted, and the prior probability distribution of the system structure parameter, root are set according to historical data
According to the prior probability point of the prediction error variance of single measuring point acceleration responsive intrinsic mode function described in gaussian probability profile set
Cloth, thus set the model parameter vector prior probability distribution p (θ | Mk)；
S2, the system structure that single measuring point is decomposed using Empirical mode decomposition respond to obtain its intrinsic mode function,
Utilize the probability density estimation of the intrinsic mode function structure forecast error vector；
Specifically, the specific implementation method of step S2 includes：
Assuming that the model output of structure is expressed as model (θ), corresponding system output is expressed as system, then predicting
Error vector can be calculated by e=system-model (θ), according to principle of maximum entropy, predict the probability density function of error vector
Model is the Gaussian Profile for having zero-mean and covariance matrix, is constructed using the intrinsic mode function of single Measuring Point Structure response pre-
Survey the probability density estimation of error vector：
Wherein i=1 ..., the serial number of n expression intrinsic mode functions, subscript l=1 ..., NeIndicate the sequence of observation experiment
Number, subscript r indicates single Measuring Point Structure response, can be acceleration (a), speed (v) or dynamic respond (d),It is first
The prediction error vector of i-th of intrinsic mode function of single Measuring Point Structure response in observation experiment, No is the degree of freedom observed
Quantity,For the prediction error variance of i-th of intrinsic mode function of single Measuring Point Structure response, teIndicate the time point measured
Quantity, t indicate the time point serial number measured,It is the of the structural response that t moment in first of observation experiment observes
I intrinsic mode function, IMFi mr(θ, t) is the model value of i-th of intrinsic mode function of the structural response of t moment,For list
The prediction error variance of i-th of intrinsic mode function of Measuring Point Structure response；
S3, Definition Model group parameter set a series of model groups to be selected, and close using the probability of the prediction error vector
Spend the likelihood function that function model derives construction Bayesian model；
Specifically, the specific implementation method of step S3 includes：
Definition Model group parameter：
Wherein standard deviationStd () indicates the standard deviation of signal.For a series of models
Group M, the factor η and ρ can define a series of model group M={ M to be selectedk=M (η (k), ρ (k)):K=1 ..., Nc,
Assuming that the prediction error of system response is statistically independent of one another, then likelihood function can be expressed as
Wherein overall fit measure definitions are
C is mark Huaihe River constant, can be derived and be calculated according to formula (1)-(3)；
S4, the intrinsic mode function obtained based on the decomposition, are applied to gradation type by the likelihood function derived
Markov chain Mondicaro (TMCMC) algorithm designs Bayesian model update method, based on the system structure for detecting and obtaining
Response updates the prediction error of the system structure parameter and single measuring point acceleration responsive intrinsic mode function of the model group to be selected
The prior probability distribution of variance, the posteriority for calculating the corresponding normalized parameter of each model group to be selected and model parameter are general
Rate is distributed, and is finally acquired most probable model group by Bayesian model method for selecting, is obtained the corresponding system of the most probable model group
The Posterior probability distribution of system structural parameters；
Specifically, the specific implementation method of step S4 includes：
On the basis of likelihood function model, according to Bayes principle, the Posterior probability distribution of model parameter vector can be by
Following formula is derived：
Wherein p (θ | Mk) be model parameter vector priori probability density function, p (D | Mk) it is normalized parameter；
Formula (3)-(5) are applied to gradation type Markov chain Mondicaro (TMCMC) algorithm, to a series of model group bases
In the system structure response progress Bayesian model update for detecting and obtaining, the corresponding normalization of each model group can be obtained
The Posterior probability distribution of parameter and model parameter；
It is assumed that all model groups have equally probable prior probability, then the probability density function of prior distribution is by p (Mk
| M)=1/NcIt calculates, and normalized parameterOn this basis, by Bayes's mould
Type method for selecting：
Most probable model group can be acquired, the Posterior probability distribution { θ of the corresponding system structure parameter of the model group is obtaineds,h:h
=1 ..., Ns, subscript h indicates to follow the serial number of the structural parameters sample of Posterior probability distribution；
S5, referred to according to the damage of the Posterior probability distribution structural texture of the corresponding system structure parameter of the most probable model group
Mark, judges structural damage.
Specifically, the specific implementation method of step S5 includes：
In view of the different damage modes of structure, structure is obtained under different damage modes by the step S1 to S4
The Posterior probability distribution of the corresponding system structure parameter of most probable model groupComparison structure is not
The posterior probability density function for the corresponding system structure parameter of most probable model group estimated under degree of impairmentStructural texture damage criterion IOD (Index of damage) judges the position of structural damage
And degree of injury：
Wherein, subscript j=1 ..., NdIndicate different damage modes.
The present invention provides a kind of Structural Damage Identifications based on Bayesian model, can be applied to multi-Degree-of-Freedom Linear
The structural parameter identification of time-varying system and small nonlinearity time-varying system.The parameter identification method of traditional time-invariant system is often adopted
Likelihood function is constituted with the intrinsic frequency and Mode Shape of system, the present invention proposes novel likelihood function model, uses list
The time-varying intrinsic mode function tectonic model likelihood function of Measuring Point Structure response, time-varying intrinsic mode function can be easily from corresponding
The empirical mode decomposition of structural response obtains, and can be used for solving the parameter identification problem of general time-varying system, significantly reduces meter
Calculate complexity；Meanwhile the present invention uses gradation type Markov chain Mondicaro algorithm in Bayesian model renewal process, keeps away
The problem directly sampled from Posterior probability distribution is exempted from, from a series of simple intermediate probability for converging on Posterior probability distribution
It is sampled in distribution, can directly acquire the normalized parameter in model parameter Posterior probability distribution formula, improve the effect of calculating
Rate；By the structural damage method for implementing to provide in the present invention, the difficulty that structural damage is identified in Practical Project can be greatly reduced
Degree, improves the efficiency of Damage Assessment Method, economizes on resources and the time for engineering construction, makes subsequent engineering construction more smoothly and more
Rapidly carry out.
The preferred embodiment of the present invention has been described in detail above, it should be understood that those skilled in the art without
It needs creative work according to the present invention can conceive and makes many modifications and variations.Therefore, all technologies in the art
Personnel according to present inventive concept in prior art basis by logic analysis, reasoning or according to it is limited experiment it is available
Technical solution, should be among the protection domain determined by the claims.
Claims (6)
1. a kind of Structural Damage Identification based on Bayesian model, which is characterized in that this approach includes the following steps：
S1, the system structure for being detected to obtain multigroup single measuring point to mechanical structure or building structure respond；According to history number
According to the prior probability distribution of initialization system structural parameters, according to the intrinsic mode of gaussian probability profile set list measuring point acceleration responsive
The prior probability distribution of the prediction error variance of function；
S2, the system structure that single measuring point is decomposed using Empirical mode decomposition respond to obtain its intrinsic mode function, utilize
The probability density estimation of the intrinsic mode function structure forecast error vector；
S3, Definition Model group parameter set a series of model groups to be selected, and utilize the probability density letter of the prediction error vector
Exponential model derives the likelihood function of construction Bayesian model；
S4, the intrinsic mode function obtained based on the decomposition, are applied to gradation type Marko by the likelihood function derived
Husband's chain Mondicaro (TMCMC) algorithm designs Bayesian model update method, based on the system structure response for detecting and obtaining
Update the prediction error variance of the system structure parameter and single measuring point acceleration responsive intrinsic mode function of the model group to be selected
Prior probability distribution, calculate the posterior probability point of each model group to be selected corresponding normalized parameter and model parameter
Cloth finally acquires most probable model group by Bayesian model method for selecting, obtains the corresponding system knot of the most probable model group
The Posterior probability distribution of structure parameter；
S5, according to the Posterior probability distribution structural texture damage criterion of the corresponding system structure parameter of the most probable model group,
Judge structural damage.
2. the Structural Damage Identification based on Bayesian model as described in claim 1, which is characterized in that the step S1
Specific implementation method include：
Setting models group Mk(subscript k indicates the serial number of model group), it is assumed that D={ y(l):L=1 ..., NeIt is comprising NeGroup system
The observation data of response, model parameter vector θ ∈ Θ ∈ RNpBy system structure parameter and the intrinsic mode of single measuring point acceleration responsive
The prediction error variance of function is constituted, and the prior probability distribution of the system structure parameter is set according to historical data, according to height
This probability distribution sets the prior probability distribution of the prediction error variance of single measuring point acceleration responsive intrinsic mode function, by
This set the model parameter vector prior probability distribution p (θ | Mk)。
3. the Structural Damage Identification based on Bayesian model as claimed in claim 2, which is characterized in that the step S2
Specific implementation method include：
Assuming that the model output of structure is expressed as model (θ), corresponding system output is expressed as system, then predicting error
Vector can be calculated by e=system-model (θ), according to principle of maximum entropy, predict the probability density estimation of error vector
To there is the Gaussian Profile of zero-mean and covariance matrix, missed using the intrinsic mode function structure forecast of single Measuring Point Structure response
The probability density estimation of difference vector：
Wherein i=1 ..., the serial number of n expression intrinsic mode functions, subscript l=1 ..., NeIndicate the serial number of observation experiment, on
It marks r and indicates single Measuring Point Structure response, can be acceleration (a), speed (v) or dynamic respond (d),It is real for first of observation
Test the prediction error vector of i-th of intrinsic mode function of middle single Measuring Point Structure response, NoQuantity for the degree of freedom observed,For the prediction error variance of i-th of intrinsic mode function of single Measuring Point Structure response, teIndicate the time point quantity measured, t
Indicate the time point serial number measured,It is i-th of the structural response that t moment in first of observation experiment observes
Mode function is levied,For the model value of i-th of intrinsic mode function of the structural response of t moment,For single measuring point
The prediction error variance of i-th of intrinsic mode function of structural response.
4. the Structural Damage Identification based on Bayesian model as claimed in claim 3, which is characterized in that the step S3
Specific implementation method include：
Definition Model group parameter：
Wherein standard deviationStd () indicates the standard deviation of signal.For a series of models
Group M, the factor η and ρ can define a series of model group M={ M to be selectedk=M (η (k), ρ (k)):K=1 ..., Nc,
Assuming that the prediction error of system response is statistically independent of one another, then likelihood function can be expressed as
Wherein overall fit measure definitions are
C is mark Huaihe River constant, can be derived and be calculated according to formula (1)-(3).
5. the Structural Damage Identification based on Bayesian model as claimed in claim 4, which is characterized in that the step S4
Specific implementation method include：
On the basis of likelihood function model, according to Bayes principle, the Posterior probability distribution of model parameter vector can be by following formula
It derives：
Wherein p (θ | Mk) be model parameter vector priori probability density function, p (D | Mk) it is normalized parameter；
Formula (3)-(5) are applied to gradation type Markov chain Mondicaro (TMCMC) algorithm, institute is based on to a series of model groups
It states the system structure response that detection obtains and carries out Bayesian model update, the corresponding normalized parameter of each model group can be obtained
With the Posterior probability distribution of model parameter；
It is assumed that all model groups have equally probable prior probability, then the probability density function of prior distribution is by p (Mk| M)=
1/NcIt calculates, and normalized parameterOn this basis, it is selected by Bayesian model
Method：
Most probable model group can be acquired, the Posterior probability distribution { θ of the corresponding system structure parameter of the model group is obtaineds,h:H=
1,...,Ns, subscript h indicates to follow the serial number of the structural parameters sample of Posterior probability distribution.
6. the Structural Damage Identification based on Bayesian model as claimed in claim 5, which is characterized in that the step S5
Specific implementation method include：
In view of the different damage modes of structure, structure most may be used under different damage modes is obtained by the step S1 to S4
The Posterior probability distribution of the corresponding system structure parameter of energy model groupComparison structure is not being damaged
In the case of the posterior probability density function of the corresponding system structure parameter of most probable model group estimatedStructural texture damage criterion IOD (Index of damage) come judge structural damage position and
Degree of injury：
Wherein, subscript j=1 ..., NdIndicate different damage modes.
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